1. Technical Field
The present disclosure relates to a photomask and a method of fabricating the same, and more particularly, to a photomask for forming patterns repeating in two dimensions, and a method of fabricating the same.
2. Discussion of Related Art
Semiconductor devices are becoming more highly integrated by the use of finer fabrication techniques. Photoresist patterns must have a smaller critical dimension (CD) than the wavelength of irradiated light used for pattern formation to maintain the trend of increasing integration. Further, to satisfy CD requirements, the fabrication process for the photoresist patterns must provide a high resolution and an improved depth of focus (DOF) margin.
An off-axis illumination technique is widely used as a method to improve the resolution and the DOF margin. The off-axis illumination technique exposes a photoresist layer by selecting an appropriate illumination in accordance with the patterns on a photomask and adjusting the angle of an incident light to the photomask. The selection of an appropriate illumination is of great importance in the off-axis illumination technique to form a desired photoresist pattern.
U.S. Pat. No. 6,361,909 to Gau et al, entitled “ILLUMINATION APERTURE FILTER DESIGN USING SUPERPOSITION”, describes a technique to provide the design of an optimum illumination aperture through individual analysis for the optimum CD and DOF conditions. The technique is easily employed for line/space patterns or patterns having an identical pitch in terms of axes or directions, but as for two dimensional patterns having different pitches, it is difficult to select an appropriate illumination.
FIG. 1 is a plane view illustrating a conventional photomask for forming patterns repeating in two dimensions and having axes with different pitches.
Referring to FIG. 1, light-shielding patterns 20 are repeated two dimensionally on a transparent substrate 10. Each of the light-shielding patterns 20 has a length and a width that differ from each other in measurement. The length of each light-shielding pattern in a longitudinal axis L is longer than the length thereof in a short axis S. The length measured from a center point between a pair of light-shielding patterns 20 to a center point between an adjacent pair of light-shielding patterns 20 in the longitudinal axis L is defined as a longitudinal pitch Pl. Further, the length measured from a center point of one light-shielding pattern to a center point of an adjacent light-shielding pattern in the short axis S is defined as a short pitch Ps. The pitch Pl in the longitudinal axis L is greater than the pitch Ps in the short axis S.
A pitch in the light-shielding pattern is a factor used to determine a diffraction angle. The diffraction angle (θ) is given by Equation 1.sin θ=λ/P  [Equation 1]
where λ is the wavelength of an incident light, and P is the pitch.
Once can see from Equation 1 that, in a repeating pattern, the longer the pitch, the smaller the diffraction angle.
In patterns repeating in two dimensions, the respective pitches in the longitudinal axis L and in the short axis S are different so that the diffraction angle varies in accordance with each direction. Therefore, it is difficult to select an illumination suitable for transferring the photomask on a photoresist layer.
The distances between the light-shielding patterns 20 in the longitudinal axis L or in the short axis S represent a critical dimension (CD). That is, the minimum length between the light-shielding patterns 20 either in the longitudinal axis L or in the short axis S is a critical dimension (CD).
For convenience of explanation, the distances between the light-shielding patterns in the longitudinal axis L and the distances between photoresist patterns corresponding to the light-shielding patterns in the longitudinal axis L are defined as a longitudinal CD (CDL), and the distances between the light-shielding patterns in the short axis S and the distances between photoresist patterns corresponding to the light-shielding patterns in the short axis S are defined as a short CD (CDS).
The pitch Pl in the longitudinal axis L is small relative to the length of the light-shielding patterns in the longitudinal axis L, and thus, a duty ratio, which represents a ratio of a width of the pattern relative to a pitch, is very high. If the duty ratio is high, the image sharpness of the light-shielding patterns transferred on the photoresist is reduced.
Generally, light-shielding patterns on a transparent substrate have a standard deviation associated with a desired CD, and photoresist patterns also have a standard deviation associated with a desired CD. Therefore, the light-shielding patterns need to have an allowable CD. The allowable CD is determined by a mask error enhancement factor (MEEF), which has a direct relationship with the allowable CD. In the case that the light-shielding patterns cannot be formed with a small CD due to a large MEEF, it will be difficult to form photoresist patterns with a desired CD. Therefore, in order to obtain photoresist patterns with a desired CD, the image sharpness of the light-shielding patterns transferred on the photoresist patterns should be increased to reduce the MEEF.
FIG. 2 is a simulation view illustrating an aerial image formed by using a conventional photomask. The simulation was performed by a vector model, and the wavelength of an incident light was 248 nm, and a numerical aperture (NA) was 0.7.
Referring to FIG. 2, photoresist patterns 20a corresponding to the light-shielding patterns 20 of FIG. 1 are formed on a semiconductor substrate 10a. The duty ratio of the light-shielding patterns 20 is high, and the image sharpness of the light-shielding patterns 20 is small so that the longitudinal CD (CDL) of the light-shielding patterns 20 cannot be reduced to less than a predetermined critical dimension. Therefore, the photoresist patterns 20a corresponding to the light-shielding patterns 20 are shortened in the longitudinal axis L so that the longitudinal CD (CDL) of the photoresist patterns 20a is increased.
A method of forming additional light-shielding layers on the light-shielding patterns 20 on the photomask may be employed to reduce the CDL by adjusting the length of the photoresist patterns 20a. However, the CDL can only be reduced to an extent limited by the CD of the additional light-shielding layers.
Further, when the MEEF is high, the formation of additional light-shielding layers cause bridges between the photoresist patterns and result in increased defects of the photoresist patterns.
Accordingly, there is a need for a photomask including patterns repeating in two dimensions that form photoresist patterns having a desired CDL.